Defect Formation and Kinetics of Atomic Terrace Merging

Pairs of atomic scale terraces on a single crystal metal surface can be made to merge controllably under suitable conditions to yield steps of double height and width. We study the effect of various physical parameters on the formation of defects in a kinetic model of step doubling. We treat this manifestly non- equilibrium problem by mapping the model onto a 1-D random sequential adsorption problem and solving this analytically. We also do simulations to check the validity of our treatment. We find that our treatment effectively captures the dynamic evolution and the final state of the surface morphology. We show that the number and nature of the defects formed is controlled by a single dimensionless parameter $q$. For $q$ close to one we show that the fraction of defects rises linearly with $\epsilon \equiv 1-q$ as $0.284 \times \epsilon$. We also show that one can arrive at the final state faster and with fewer defects by changing the parameter with time.